A076981 Smallest k such that n*(n+1)*(n+2)*...*(n+k) is divisible by the product of primes up to n.

0, 0, 1, 2, 1, 4, 3, 6, 5, 4, 4, 10, 9, 12, 11, 10, 9, 16, 15, 18, 17, 16, 15, 22, 21, 20, 19, 18, 17, 28, 27, 30, 29, 28, 27, 26, 25, 36, 35, 34, 33, 40, 39, 42, 41, 40, 39, 46, 45, 44, 43, 42, 41, 52, 51, 50, 49, 48, 47, 58, 57, 60, 59, 58, 57, 56, 55, 66, 65, 64, 63, 70, 69

Offset: 1

Author

Amarnath Murthy, Oct 23 2002

Keywords

• nonn

Examples

			a(8) = 6 as 8*9*10*11*12*13 is not divisible by 2*3*5*7 but 8*9*10*11*12*13*14 is.
		

Programs

Mathematica

a[n_] := For[k = 0, True, k++, If[Divisible[Pochhammer[n, k+1], Times @@ Select[Range[2, n], PrimeQ]], Return[k]]]; Array[a, 73] (* Jean-François Alcover, Oct 07 2016 *)

PARI

a(n)=if(n<0,0,k=0; while(prod(i=0,k,n+i)%prod(v=1,precprime(n),if(isprime(v),v,1))>0,k++); k)

Formula

For any n, a(n)0, a(A049591(k)+3)=A049591(k)-3 etc. - Benoit Cloitre, Oct 24 2002

Extensions

More terms from Benoit Cloitre, Oct 24 2002

Offset corrected by Sean A. Irvine, Apr 24 2025